A need exists for crystal oscillators and crystal resonators having low acceleration sensitivity, see the article entitled "The Acceleration Sensitivity of Quartz Crystal Oscillators: A Review," IEEE Transactions On Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 35, No. 3, published in May 1988. As is known, piezoelectric resonators, especially devices such as AT and SC cut quartz crystal resonators, are used in a number of applications in which they are subjected to acceleration. This acceleration can be low frequency periodic and/or random vibration to which resonators are subjected while operating. Acceleration causes the resonance frequency of a crystal resonator to change and this is undesired.
It is known from the above cited article that for accelerations which are not too large, the frequency change is the scalar (dot) product of two vector quantities, the acceleration sensitivity of the resonator and the acceleration.
The acceleration sensitivity of a piezoelectric resonator depends upon two factors--the deformation produced by the acceleration and the mode shape. While the mathematical analysis is complex, the basic idea is rather simple, see, Forty-Fourth Annual Symposium on Frequency Control--1990, pps. 452-460, entitled: "On the Influence of a Fabrication Imperfection on the Normal Acceleration Sensitivity of Contoured Quartz Resonators with Rectangular Supports". At each point in the resonator, acceleration-induced deformation alters the effective elastic stiffness of the resonator, thereby incrementally affecting the resonance frequency of each mode of vibration by an amount that depends upon the mode amplitude and sign and upon the amplitude and sign of the deformation at that point. While, in the interest of simplicity, mode amplitude is treated as if it were a single quantity, it should be recognized that the mode of vibration employed may have two or even more components, all of which may contribute to the total acceleration sensitivity. Similarly, the acceleration-induced deformation will, in general, have more than one component.
The total effect on the resonance frequency of the particular mode is the algebraic sum of the incremental effects taken over the entire volume of the resonator. An important aspect of the summation is that, due to symmetry, a high degree of cancellation takes place. That is, the sum of the positive increments is very nearly equal to the sum of the negative increments. As a consequence, even small changes in the resonator mode amplitude can result in quite large changes in acceleration sensitivity.
In a conventional thickness-mode quartz crystal resonator unit, a suitable dimensioned and electrode-carrying blank, platelet, or wafer of quartz, is supported at two or more points on its periphery by metal ribbons or clips. These, in turn, are fastened to a header or base.
FIG. 1 shows a prior art resonator 10 of conventional construction having a circular quartz blank 12 with one or more electrodes 14 thereon, both on the top and bottom of the blank (bottom not shown). Each electrode 14 has an input provided by a terminal 16 which extends to the edge of the blank to which contact is made by a mounting clip 18 mounted to the base 19 of a header 20 through an insulator 21. Mounting pins 22 extend outwardly from the header, each pin making contact with one of the mounting clips 18 in its respectively connected electrode tab terminal 16. The cover 20 is hermetically sealed to the base or header 19. The enclosed volume is often filled with an inert gas such as nitrogen, or may be evacuated.
Under acceleration, the inertial forces on the blank are counteracted by the reaction forces of the support structure. Thus, the support structure directly influences the acceleration-induced deformation of the blank. Because of fabrication and manufacturing limitations, variations in support geometry from resonator to resonator are unavoidable. Since the resonator acceleration sensitivity is the difference of two nearly equal quantities, small changes in the resonator, such as would occur due to normal manufacturing tolerances, can cause large changes in resonator acceleration sensitivity, as is borne out by experience. See the article entitled "The Acceleration Sensitivity of Quartz Crystal Oscillators: A Review "IEEE Transactions On Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 35, No. 3, published in May 1988.